Common Core: High School - Geometry : Drawing Transformed Figures: CCSS.Math.Content.HSG-CO.A.5

Study concepts, example questions & explanations for Common Core: High School - Geometry

varsity tutors app store varsity tutors android store

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 83 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1

Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a triangle is in quadrant three and undergoes a transformation that moves each of its coordinate points to the left three units and down one unit, what transformation has occurred?

Possible Answers:

Rotation

Reflection

None of the other answers.

Translation

Extension

Correct answer:

Translation

Explanation:

To determine the type of transformation that is occurring in this particular situation, first recall the different types of transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Since each of the triangle's coordinates is moved to the left and down, it is seen that the size and shape of the triangle remains the same but its location is different. Therefore, the transformation the triangle has undergone is a translation.

Example Question #2 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Possible Answers:

Dilation

Rotations

Non of the others

Extension

Reflection

Correct answer:

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates  , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line  

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

Example Question #3 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , , , and  and after a transformation results in the coordinates , , , and  identify the transformation.

Possible Answers:

Rotation

Reflection

Dilation

Extension

None of the other answers.

Correct answer:

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line  

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

Example Question #4 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Possible Answers:

Dilation

Reflection

Translation

Rotation

None of the other answers.

Correct answer:

Translation

Explanation:

To identify the transformation that is occurring in this particular problem, recall the different transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Looking at the starting and ending coordinates of the rectangle,

 , and   to  , and 

Since all the  coordinates are increasing by two this is known as a translation.

Example Question #5 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 5.51.13 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #6 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the -axis take the opposite of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 6.02.01 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #7 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the  and -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Screen shot 2016 06 15 at 6.19.15 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #8 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,


Screen shot 2016 06 15 at 6.52.29 am

Therefore, the reflected triangle has coordinates at

Example Question #9 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this triangle after it is reflected across the  and -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Screen shot 2016 06 15 at 7.35.06 am

Therefore, the coordinates of the reflected triangle are

Example Question #10 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 6.40.50 am

Therefore, the reflected triangle has coordinates at

← Previous 1

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 83 Practice Tests Question of the Day Flashcards Learn by Concept
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: